MEASUREMENT  OF  MERCURY  VAPOR  PRESSURE  BY  MEANS 
OF  THE  KNUDSEN  PRESSURE  GAUGE 


BY 


CHARLES  FRANCIS  HILL 
A.  B.,  University  of  Illinois,  1914. 
A.  M.,  University  of  Illinois,  1916. 


THESIS 


SUBMITTED  IN  PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS 


FOR  THE  DEGREE  OF 


DOCTOR  OF  PHILOSOPHY 

IN  PHYSICS 

IN 


THE  GRADUATE  SCHOOL 


OF  THE 


UNIVERSITY  OF  ILLINOIS 


1921 


Digitized  by  the  Internet  Archive 
in  2015 


https://archive.org/details/measurementofmerOOhill 


UNIVERSITY  OF  ILLINOIS 


THE  GRADUATE  SCHOOL 


April  30 j 19&1 

I HEREBY  RECOMMEND  THAT  THE  THESIS  PREPARED  UNDER  MY 

SUPERVISION  BY.  CHARLES  FRA1ICIR  HILL 

entitled__jJ£asiiril:e;:t,  qf^lzrcury  va;-cr,.?.ri:s.sury  ey  izats 

OF  THE  KiUDSE::  pressure  gauge 

BE  ACCEPTED  AS  FULFILLING  THIS  PART  OF  THE  REQUIREMENTS  FOR 


Recommendation  concurred  in* 


Committee 


on 


Final  Examination* 


*Required  for  doctor’s  degree  but  not  for  master’s 


4-?'^G£  9 


■ 


. 


- • ' > - 


1 


TABLE  OF  CONTENTS 


I.  INTRODUCTION  

II.  HISTORICAL 

1.  Dalton  

2.  Avcgadrc  

0.  Regnault  

4.  Hertz  

5.  Van  der  Plaats  

a.  Table  I 

8.  Hagen  

7.  Ramsey  and  Young 

8.  Morley  

9.  Knuds en  

10.  Comparison  of  Previous  Methods  .... 

III.  experimental 

1.  Description  of  Apparatus  and  Method 

2.  Discussion  of  Accuracy  of  Method  . . 

3.  Comparison  with  Previous  Methods. . . 

4.  Data  - Tables  II  to  IX  

5.  Curves  

IV.  CONCLUSIONS  


1 

2 

2 

2 

3 

3 

4 

5 

6 

6 

7 

9 

10 

14 

15 

17 

24 

28 


I.  INTRODUCTION 


Within  the  last  thirty  years,  a large  amount  of  research  ha3 
been  done  in  partial  vacua  requiring  an  accurate  knowledge  of  the 
gas  pressure.  Mercury  and  oil  pumps  have  been  used  in  the  production 
of  these  vacua,  and  the  gas  pressure  has  been  measured  by  means  of 
the  McLeod  gauge.  Now  the  total  gas  pressure  must  necessarily  in- 
clude the  vapor  pressures,  and  as  is  well  known,  the  McLeod  gauge 
does  not  measure  vapor  pressure.  Liquid  air  or  other  cold  agents 
are  usually  applied  to  remove  vapors.  Often  several  hours  are  re- 
quired to  do  this,  due  to  the  fact  that  large  quantities  of  vapor 
are  absorbed  by  the  walls  of  the  container.  In  the  case  of  mercury 
and  vacuum  oils  a free  surface  is  usually  exposed  to  the  vacuum  and 
hence  only  an  equilibrium  condition  between  evaporation  and  conden- 
sation can  be  reached.  It  has  been  found  in  the  present  experimental 
work  that  this  equilibrium  condition  may  be  as  much  as  one-third  or 
even  two-thirds  of  the  saturation  pressure,  depending  upon  the  amount 
of  surface  exposed.  Experimenters,  generally,  have  probably  not 
realized  the  difficulty  of  removing  all  vapors.  If  the  saturation 
pressures  of  these  vapors  are  accurately  known,  especially  for  mercu- 
ry, it  would  be  of  value  in  vacuum  experiments.  Most  of  the  pub- 
lished data  on  the  vapor  pressure  of  mercury  at  temperatures  ranging 
from  0°  to  50°  is  merely  extrapolated  from  values  at  high  tempera- 
tures. Only  three  direct  methods  have  been  used  over  the  range  0° 
to  50°,  and  these  show  a lack  of  agreement,  the  variations  being  a 
large  percent.  The  methods  employed  are  also  open  to  question  due 
to  evident  sources  of  error.  Because  of  the  meagerness  of  the  data, 
and  the  lack  of  agreement  between  the  different  observers,  it  was 
decided  to  attempt  a redetermination  of  the  vapor  pressure  of  mercury 


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between  the  temperatures  of  0°  and  40° C.  The  use  of  the  Knudsen 
pressure  gauge  was  considered  the  most  dependable  method,  since  this 
instrument  is  independent  cf  the  gas  and  measures  pressures  of  the 
order  of  mercur*  vapor.  The  results  obtained  with  the  instrument 
are  given,  following  a brief  review  of  the  methods  and  results  of 
previous  observers. 

II.  HISTORICAL 

That  mercury  has  a vapor  pressure  was  discovered  about  1796 
by  investigators^  in  Holland.  Dalton  also  discovered  the  fact  soon 
I after  and  even  made  a few  measurements  at  high  temperatures  before 
1802.  It  was  shown  that  mercury  could  be  evaporated  at  fairly  low 
temperatures  but  at  temperatures  of  about  20° C,  many  thought  that 
the  vapor  pressure  was  zero.  In  some  experiments  about  1824,  Fara- 
day placed  some  gold  foil  over  mercury.  The  foil,  in  the  course  of 
a few  hours  disappeared,  and  in  his  explanation  of  the  result,  he 
attributed  tne  effect  as  due  to  some  sort  of  an  affinity  between  the 
gold  and  the  mercury  and  not  to  the  evaporation  cf  the  mercury.  This 
view  that  the  vapor  pressure  was  zero  at  lew  temperatures,  seems  to 

have  been  rather  general  until  about  1850. 

I _ 3 

In  1833,  using  temperatures  between  2b0°  and  300°,  Avagadro 

made  measurements  on  the  vapor  pressure  cf  mercury  in  a barometer 
tube.  Using  Dalton’s  equation,  P = ab^,  he  extrapolated  back  to 
0°;  however,  over  such  a long  range  the  extrapolation  would  have  but 
little  value,  and  it  is  now  known  that  Dalton's  equation  does  not 

1.  J.R.  Dieman,  Van  trost  Wijk,  Bondt.  Chemische  and  Physische 
Oefanngen,  18S7. 

2.  Phil.  Trans. , 1826. 

3.  Ann.  de  Pogg. , 


1833,  T27,  p 60. 


. 


1 

. 


3 


hold  except  for  the  region  in  which  its  constants  are  determined. 

Regnault^,  using  practically  the  same  method,  made  measure- 
ments in  1862  at  temperatures  above  100c ; he  had,  however,  consider- 
able trouble  in  getting  readings  at  the  lower  temperatures.  Regnault 
used  the  empirical  equation  cf  Biot, 

Leg  P = a + bC^  + cK*1 , 

and  extrapolated  to  0°.  His  results  over  the  range  0°  to  40°  are  now 
known  to  be  10  to  100  times  too  large  since  values  which  he  gives  can 
be  measured  accurately  by  later  methods. 

About  1880,  due  to  the  invention  of  the  Toepler  and  Sprengel 
air  pumps  and  also  the  McLeod  gauge,  the  question  cf  the  vapor  press- 
ure of  mercury  became  of  greater  importance.  Rood  claimed  .000002mm. 
for  the  Sprengel  pump,  ana  Hagen  .00001  mm.  for  the  Toepler  pump.  If 
mercury  had  an  appreciable  vapor  pressure,  this  fact  would  have  a de- 
cided influence  upon  the  resultant  pressures  reached  by  the  pumps. 

Several  investigations  were  car- 
ried out  immediately  and  published 

between  the  years  cf  1880  and  188S. 

5 

Among  the  first  was  that  cf  Hertz  , 
his  measurements  being  considered  as 
among  the  mere  accurate  ones  made  at 
higher  temperatures.  The  apparatus 
used,  consisted  of  a differential  manometer  as  shown  in  Fig.l.  The 
system  was  pumped  out  and  closed.  Then  A was  placed  at  the  desired 
temperature,  which  caused  a difference  in  level  of  the  two  arms  of 


4.  Memoirs  de  I'nstitute,  1862,  T 26,  p 506. 

5.  Wied.  Ann.,  15,  Vol.17,  p 193. 


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4 


the  manometer  C.  By  letting  in  air  until  the  two  arms  of  C balanced, 

the  vapor  pressure  of  mercury  could  be  read  as  the  difference  in  the 

heights  of  the  two  arms  of  B.  The  temperature  range  was  frcrr  89.4"  to 

206p  C.  hertz  used  the  theoretical  equation, 

i — s— c -W  T 

P = KT"  irp  e w by  means  of  which  an 
extrapolation  was  made  to  zero.  While  tne  equation  has  some  theo- 
retical foundation,  the  constants  are  all  calculated  by  applying  the 
equation  to  the  data,  and  all  of  the  quantities  become  experimentally 
determined.  Hertz  took  readings  below  89.4°  but  did  net  consider  them 
since  his  error  was  of  the  order  of  magnitude  of  the  quantities 
measured.  Even  at  117°  his  error  was  ¥jo  from  the  mean,  and  errors  at 
the  lew  points  affect  extrapolated  values  to  a great  extent,  especially 
when  the  values  sought  are  as  small  as  those  of  mercury  vapor,  and  tin 
extrapolation  is  over  a long  range. 

L 

In  1886,  van  der  Plaats  published  results  by  taking  readings 
in  the  temperature  range  of  0°  to  20°  C,  a region  in  which  no  other 
data  had  been  taken  except  that  of  Hagen.  While  the  percent  error  cf 
nis  measurements  is  comparatively  large,  the  data  must  be  given 
considerable  weight  since  the  method  was  direct.  Values  from  his 
mean  curve  have  been  given  preference  in  tables,  probably  due  to  the 
fact  that  the  method  was  direct.  Van  der  Plaats’  obtained  his  read- 
ings by  passing  dry  gas  through  water,  through  sulphuric  acid,  and 
then  through  mercury  until  saturated,  after  which  the  mercury  was 
collected  by  means  of  geld  and  pumice  stone.  The  amount  of  water  and 
mercury  collected  was  weighed.  Knowing  the  volume,  temperature,  and 
pressure  of  the  gas,  and  the  vapor  pressure  cf  water  he  could  calculate 


6.  Rec.  Trans.  Chim.  5,  p 49,  1886. 


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' 


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5 


vapor  pressure  of  the  mercury.  Van  der  Plaats'  readings  show  consid- 
erable variation,  nevertheless  they  are  consistent  enough  to  indi- 
cate that  the  order  must  be  correct.  The  readings  are  given  below. 


Temperature 


0° 

. 00042 

4° 

. 00058 

7C 

. 00071 

9° 

. 00073 

10° 

. 00077 

11° 

.00083 

12° 

. 001C1 

15° 

.001 

14° 

.00101 

16° 

.00115 

18° 

.00133 

20° 

. 00133 

Pressure 

.000515  .00048  .00044 

.00084  .000735 

.00058 
. 00093 


It  is  readily  seen  that  if  two  or  three  values  are  omitted 
the  others  fall  within  +15/o  of  the  mean  curve.  His  error  could  be 
accounted  for  by  the  small  quantities  of  collected  mercury  that  he 
had  to  measure.  Otherwise,  the  method  seems  difficult  to  criticise; 
however,  it  should  net  give  values  too  high. 

7 

In  1882,  Hagen  published  results  which  he  got  by  taking 

readings  between  0°  and  200°,  in  50° 
steps.  The  apparatus  is  shown  in  Fig. 2. 
The  system  was  pumped  while  heating  in 

t 

order  to  rid  the  walls  of  vapors  and  gas- 
es, after  which  the  mercury  was  admitted 
through  the  capillary  at  the  bottom. 

After  the  pressure  had  come  into  equi- 
librium, the  tubes  at  the  points  E and  F 
were  sealed  off.  The  mercury  then  stood 


7.  Wied.  Ann.,  1882,  Vol.lS,  p 610, 


6 


at  the  same  level  at  A and.  B.  By  raising  the  whole  apparatus  to  a 
temperature,  T,  the  space  above  the  mercury  became  saturated  with 
vapor.  If  C was  now  placed  in  carbon  dioxide  snow  and  ether,  Hagen 
thought  that  all  of  the  vapcrs  would  be  removed  and  the  difference 
in  pressure  read  between  the  heights  of  the  two  branches,  A and  B, 
would  thus  be  tne  vapor  pressure  of  mercury.  This  difference  was 
read  by  means  of  a cathetometer.  What  Hagen  measured,  of  course, 
was  an  equilibrium  condition  between  evaporation  and  condensation. 

His  values  should  therefore  be  too  low.  However,  his  results,  like 
those  of  Regnault,  are  10  to  100  times  too  high.  His  data  also  in- 
creases about  20%  from  0°  to  20°  and  40%  from  90c  to  100°,  while 
vapor  pressures,  as  is  well  known,  should  have  a decreasing  percent 
increase  as  the  temperature  increases. 

Q 

Another  important  set  of  data,  that  of  Ramsey  and  Young  , was 
published  in  1886.  The  relation  of  the  absolute  temperatures  of  wa- 
ter and  mercury  for  which  the  two  have  the  same  vapor  pressure,  is 
well  enough  known  sc  tnat  if  a few  values  are  determined  the  ones 
between  may  be  calculated.  They  applied  this  principle,  getting 
readings  from  135°  to  520°C.  , and  then  extrapolated  to  zero,  using 
Regnault 1 s equation.  At  the  high  temperatures,  the  results  of 
Ramsey  and  Young  and  those  of  Hertz  agree  very  closely.  Ramsey  and 
Young,  however,  used  a much  greater  tenperature  range,  and  thus  theii 

data  should  give  a more  accurate  extrapolation. 

o 

In  1904,  E.W.  Morley*  used  a method  similar  to  that  of  Van 
der  Plaats,  except  that  the  evaporated  mercury  was  determined  by 
weighing  the  whole  mercury  sample  before  and  after  exTaporat ion,  and 

8.  Journal  Chem.  See. , 1886,  49,  p 37. 

9.  Phil.  Mag. , 


1904,  p 662. 


7 


the  difference  taken.  He  made  determinations  at  temperatures  18  r , 

30° , 40°,  50°,  60°,  and  70°,  and  calculated  a mean  curve  by  means  of 
Dalton's  formula, 

P = ab  ^ . 

Morley's  readings  at  16°,  30°,  and  40°  are  from  8 Jo  to  20 fo  below  his 
mean  curve,  hence  it  appears  that  his  extrapolated  values  can  not  be 
depended  upon  to  be  so  very  accurate.  Again,  the  uniform  slope  of 
the  curve  is  net  in  agreement  with  what  one  would  expect  for  vapor 
pressure  curves;  however,  the  small  amount  of  data  and  the  variation 
of  the  lower  points  could  easily  account  for  this.  The  variation  at 
the  low  temperatures  is  not  surprising  if  one  considers  that  he  musl 
detect  a less  of  4.5  mg.  of  mercury  from  a large  sample  of  mercury, 
even  after  a run  of  13  days. 

The  last  data  of  importance  published  was  that  of  KnudsenJ‘J 

in  1909.  Knudsen  first  developed  an  equation*'1'  for  the  flow  of  a 

12 

gas  through  a tube  in  a time  t.  Later,  this  equation  was  extended 
to  the  case  of  a tube  with  a plate  over  one  end,  the  plate  contain- 
ing a small  opening  so  that  the  resistance  to  flow  was  mostly  at  the 

opening.  His  equation  is  as  follows, 

_ - P'-P” 

G “ wx+w2 

where  G is  the  mass  of  gas  that  passes  through, is  the  density  at 
the  temperature  considered,  P'  and  P"  are  the  pressures  at  the  ends 
of  the  tube,  W1  and  W are  the  resistances  of  the  tube  and  opening, 
and  t is  the  time.  W*  and  W"  are  calculated  from  dimensions  and  are 
gotten  from  theoretical  considerations.  Apparatus,  based  upon  the 


10. 

Ann. 

der 

Physik, 

lb 09 , 29,  p 

179. 

• 

H 

rH 

Ann. 

der 

Physik, 

1908-9,  28, 

p 75. 

12. 

Ann. 

der 

Physik, 

1S08-9,  28, 

p 999. 

. 

I 


I 


8 


above  theory  was  then  developed  by  which  the  vapor  pressure  of  mercu- 
ry could  be  determined.  This  apparatus  is  shown  in  Fig. 3.  A glass 

tube  with  mercury  placed  as  shown  is  evacuated 
and  then  sealed  off.  The  small  opening  is 
placed  between  the  two  compartments,  A and  B. 

A is  placed  in  a temperature  bath  while  B is 
kept  at  a low  temperature  by  means  of  carbon 
dioxide  snow  and  benzol.  P%  the  pressure  in 
B,  is  considered  zero  since  the  vapor  pressure 
of  mercury  at  this  low  temperature  would  be 
negligible.  The  mass  of  vapor  that  passes 
through  in  a time  t is  then  measured.  In  the 
equation,  the  pressure  P'  is  considered  that 
at  the  opening  and  to  be  the  vapor  pressure  of 
mercury,  and  can  be  calculated  if  , W*  and  W"  are  known.  Readings 
from  0°  to  154° C were  taken. 

A criticism  of  this  method  should  include  a criticism  of  both 
the  theory  and  the  experimental  method.  With  the  weight  of  evidence 
of  other  methods  indicating  that  his  results  are  too  low,  the  equa- 
tion should  certainly  be  tested  further  before  great  weight  can  be 
given  to  uhe  results.  The  method  tends  to  give  values  too  low*  An 
appreciable  time  is  required  for  mercury  to  evaporate,  and  since  P* 
is  continually  being  relieved,  this  would  tend  to  give  a value  below 
that  of  the  saturation  pressure.  Any  residual  gas  in  the  tube  would 
also  hinder  diffusion  and  thus  lower  the  calculated  value. 

All  otner  values,  except  the  extrapolated  values  of  Hertz, 
are  far  above  those  of  Knudsen  over  the  range  from  0C  to  30rC. . 
Xnudsen's  curve  has  the  greatest  slope  of  any  ether  investigator. 


9 

and,  although  lowest  at  0°  is  highest  at  154°,  his  highest  tempera- 
ture measured. 

in  order  to  compare  results,  the  following  table  is  given. 
Pressure  is  expressed  in  miliirr.et ers  of  mercury. 

TABLE  I 


T 

Regnault 

Hagen 

Hertz 

Rams  ey 
Young 

Van  der 
Plaats 

Morley 

Knudsen 

Hill 

0° 

.03 

.015 

.00019 

. 00047 

.0004 

. 000184 

. 00035 

10° 

.0268 

.018 

, 0005 

. 0008 

. 0008 

.0005 

. 000775 

20° 

.0372 

.021 

. 0013 

. 0013 

.0015 

.00118 

.00182 

30° 

.053 

.026 

.0029 

.003 

.00273 

. 00407 

40° 

.0767 

. 0 33 

.0063 

.008 

. 006 

.006 

.00787 

50° 

. 112 

.042 

.013 

.015 

.011 

.0126 

. 0080C 

60°  .021 

70°  . 04 

Regnault’s  and  Hagen’s  data  agree  fairly  well,  but  both  are  now 
known  to  be  too  high  since  values  as  large  as  they  give  could  be 
readily  measured  by  later  methods.  At  higher  temperatures  of  100° 
and  above,  the  results  of  Ramsey  and  Young,  and  those  of  Hertz  differ 
by  only  a small  percent,  and  either  is  probably  within  a small  per- 
cent of  the  correct  values  at  those  high  temperatures.  Hertz  dis- 
carded his  readings  below  about  90°  because  his  error  was  large  com- 
pared to  the  magnitude  measured.  Errors  in  his  lowest  temperature 
readings  would  affect  his  extrapolated  values  to  a large  extent. 
Ramsey  and  Young  used  a wider  temperature  range  but  their  lowest 
point  was  135° C. , which  gives  them  a longer  extrapolation.  The 
weight  of  the  two  sets  of  data  would  probably  be  about  the  same. 

Knudsen  used  a direct  method  over  a range  from  0°  to  154°  and 
obtained  consistent  results.  His  data  also  agree  with  the  extra- 
polated values  of  Herts.  However,  his  method  would  tend  to  give 
values  too  low.  The  methods  of  Morley  and  van  der  Plaats,  would 
also  be  expected  to  give  results  too  lew  if  in  error,  and  yet  they 
are  about  two  or  three  times  as  high  as  Knudsen' s,  and  agree  fairly 


I 


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10 


well  with  each  other,  and  with  the  results  of  Ramsey  and  Young  and 
with  the  data  taken  in  the  present  experimental  work.  While  van  der 
Plaate  and  Mcrley  can  not  claim  a high  percent  of  accuracy  due  to 
the  error  in  observations,  yet  their  method  would  not  be  expected  to 
be  in  error  by  as  much  as  Knudsen's  data  indicates. 

The  conclusion  from  the  above  discussion  is,  that  the  weight 
of  experimental  evidence  seems  to  indicate  that  the  correct  values 
for  the  vapor  pressure  of  mercury  are  probably  of  the  order  of  the 
data  taken  by  Morley  and  van  der  Plaats. 

III.  EXPERIMENTAL 

After  noting  the  disagreement  of  previous  observations,  it  is 
evident  that  a set  of  measurements  by  a direct  and  dependable  method 
at  ordinary  working  temperatures  would  be  worth  while.  The  Knudsen"^ 
pressure  gauge,  if  accurately  calibrated,  will  give  consistent  and 
accurate  readings  on  pressures  of  the  magnitude  of  mercury  vapor  and 
has  been  used  as  low  as  10“®  mm.  The  instrument  may  be  used  as  an 
absolute  manometer;  however,  the  one  used  in  this  case  was  not  ar- 
ranged to  be  used  in  this  manner,  -lienee  it  was  necessary  to  cali- 
brate it  by  means  of  seme  other  gauge.  The  principle  upon  which  it 
depends  is  that  if  a strip  of  platinum,  say,  is  heated  in  a partial 
vacuum,  the  molecules  of  the  residual  has  will  become  heated  by  con- 
tact with  the  strip  and  fly  off.  If  a vane  free  to  turn  is  placed 
before  the  heated  strip,  these  molecules  will  strike  and  turn  the 
vane,  if  the  mean  free  path  of  the  molecules  is  greater  than  the 
distance  between  the  vane  and  foil.  The  pressure  is  proportional 
to  the  number  of  molecules  present  and  thus  the  deflection  gives  a 
measurement  of  the  pressure.  Now  the  deflection  at  zero  pressure 

13.  Ann.  der  Physik,  1910,  32,  4,  pp  809-43;  Phys.Rev.  12,  pp  70- 
30,  1918. 


11 

is  zero,  so  if  the  pressures  are  read  on  another  gauge  and  the 
deflections  on  the  Knudsen  gauge,  curves  may  he  drawn  with  the  ori- 
gin as  an  accurately  determined  point.  This  fact  made  it  possible 
to  use  a McLeod  gauge  for  calibration,  since  it  may  be  read  fairly 
accurately  to  about  .0005  mm. 

A special  Pyrex  McLeod  gauge  was  made  for  the  purpose.  This 
was  desirable  since  the  rest  of  the  apparatus  was  made  of  pyrex.  The 
volume  tube  was  made  rather  large  so  as  tc  do  away  with  friction  and 
surface  tension  of  the  mercury  as  much  as  possible.  The  gauge  would 
still  read  consistently  to  .0005  mm.  if  the  mercury  and  glass  were 
kept  clean.  The  apparatus  was  connected  as  shown  in  Fig. 4.  The 
Knudsen  gauge.  A,  and  the  sample  container,  B.  were  fixed  rigidly  in 
a tight  box  at  1,2,3,  so  that  the  calibration  would  remain  constant 

and  the  temperature  could  be  con- 
trolled. A tube  led  off  to  the 
liquid  air  trap,  tc  the  McLeod  gauge 
and  to  the  pump  as  shown.  The  pump- 
ing system  consisted  of  a Langmuir 
condensation  pump  in  series  with 
Gaede  Rotary  oil  and  mercury  pumps. 
With  all  of  the  vapors  removed  and 
kept  from  the  Knudsen  gauge  by  means 
of  liquid  air  on  the  trap,  C,  the 
pressure  was  made  about  .005  mm.  and 


then  by  reducing  the  pressure  in  steps,  reading  the  pressures  on  the 
McLeod  gauge  and  the  deflections  on  the  Knudsen  gauge,  a set  of 


calibration  curves  was  drarra.  for  the  currents  .3,  .4,  .b  and  .6 
amperes  flowing  through  the  platinum  strip.  In  order  tc  gain 


12 


accuracy,  the  curves  were  drawn  on  40  cm.  co-ordinate  paper.  Prac- 
tically all  of  the  points  fell  accurately  on  the  curves,  showing 
that  the  McLeod  gauge  was  consistent  at  least.  (See  Fig. 5 and  6.) 

The  sample  of  mercury  was  then  introduced  into  the  container 
and  with  liquid  air  on  the  trap  and  pumps  running,  the  mercury  was 
distilled  out  of  the  container  to  the  walls  of  the  tube  and  hack 
again  by  heating  slowly.  This  process  of  distillation  was  carried 
out  a number  of  times.  Then  with  warm  water  on  the  sample,  the 
whole  tube  was  heated  to  a temperature  of  350°  to  300°C.  for  several 
hours,  to  drive  the  vapors  and  absorbed  gases  out  of  the  walls  of 
the  tube.  The  apparatus  was  then  sealed  off  at  E.  The  vapor  press- 
ure of  mercury  at  any  temperature  may  be  gotten  by  allowing  the  sys- 
tem to  reach  a constant  temperature  for  a time,  taking  the  total 
pressure,  and  then,  after  driving  in  all  of  the  vapor  by  heating, 
with  liquid  air  on  the  sample  container,  measure  the  residual  press- 
ure. 

The  difference  between  the  total  and  residual  pressures  is 
the  vapor  pressure  of  mercury.  In  this  way  readings  were  taken  at  a 
number  of  temperatures  between  0°  and  35° C. , and  the  tube  was  again 
opened  and  the  same  process  of  distillation  and  heating  carried  out 
and  tiie  tube  sealed  off  again.  This  process  was  continued  until 
minimum  values  for  the  vapor  pressure  of  mercury  were  obtained  on 
three  successive  sets  of  readings.  It  was  thought  that  the  mercury 
could  be  considered  pure  at  this  point.  Another  calibration  of  the 
gauge  was  now  carried  out  and  a second  sample  of  mercury  purified 
with  nitric  acid  was  introduced  and  the  process  of  distillation  and 
heating  repeated.  The  readings  on  this  sample  checked  within  a small 
percent  cf  the  three  readings  on  the  first  sample.  Of  the  four  sets 


' * ' ! t > 


■ - 


13 


of  data,  one  or  two  points  differ  from  a mean  curve  by  about  6^>,  the 
rest  are  all  within  +3$,  which  is  about  the  accuracy  one  would  ex- 
pect from  the  method,  as  will  be  shown  later. 

Using  the  above  method,  the  vapor  pressure  of  mercury  was 
measured  at  nineteen  points  between  the  temperatures  of  -.7°  and 
34. 9° C.  The  temperature  was  measured  by  means  of  two  tenth-degree 
thermometers,  placed  at  different  points  in  the  box.  To  insure  a 
uniform  temperature,  the  air  was  circulated  by  a fan  within  the  box 
but  driven  by  a motor  outside,  the  whole  fan  system  being  entirely 
disconnected  from  the  box  and  the  pier  supporting  it.  This  was 
necessary  to  prevent  jarring  of  the  Knuds en  gauge.  Bafflers,  H,  were 
introduced  to  direct  the  circulation  of  the  air. 

The  regulation  of  temperature  was  easily  accomplished.  For 
those  above  room  temperature,  two  heating  coils,  D,  were  used, 
through  which  the  current  could  be  controlled.  For  those  below  room 
temperature,  the  window  was  opened  and  an  electric  fan  made  to  blow 
air  on  the  box,  -.7°  being  reached  in  this  way,  the  unusually  warm 
winter  preventing  lower  temperatures.  An  attempt  was  made  to  control 
the  low  temperatures  by  turning  the  nozzle  of  a carbon  dioxide  tank 
into  the  box  but  this  lacked  constancy.  In  general  the  temperatures 
were  held  very  constant,  probably  to  within  +. 1°  , or  at  most  to  ±.  2° . 
If  the  thermometer  changed  as  much  as  .2  the  change  was  detected  on 
the  Knuds en  gauge;  and  it  is  doubtful  if  the  apparatus  would  change 
as  readily  as  the  thermometers. 

The  Knuds en  gauge  was  read  by  means  cf  a lamp  and  scale  at 
about  one  meter  distance.  In  order  to  hold  the  zero  point,  or  rather 
to  hold  tne  vane  and  foil  at  constant  distance,  the  scale  was  rigidly 
fixed  to  the  floor.  Whenever  the  vane  became  displaced,  it  could  be 


• 

■ 

• 

. 

. 

14 


brought  back  to  its  zero  point  by  merely  restoring  the  zero  point  of 
the  scale.  One  set  of  calibration  curves  was  used  for  three  sets  cf 
data,  and  between  each  set  the  calibration  was  checked,  so  that  it 
was  known  to  remain  constant. 

Before  comparing  the  present  data  with  that  of  former  observ- 
ers, it  would  probably  be  best  to  consider  some  of  the  sources  of 
error  in  this  research  and  their  magnitudes.  In  the  first  place  the 
method  would  be  expected  to  give  values  too  high,  since  all  impuri- 
ties would  tend  to  increase  the  vapor  pressure  in  the  tube.  Hence, 
the  first  sample  of  mercury  was  distilled  more  than  twenty  times  in 
a vacuum,  probably  95 $ of  the  sample  being  lost.  The  second  sample 
was  first  treated  with  nitric  acid  and  then  distilled  8 times  with 
the  pump  running.  The  data  on  it  checked  within  a small  percent  of 
the  mean  curve  of  the  first  sample.  This  indicates  that  the  error 
due  to  other  vapors  was  negligible.  It  was  thought  that  the  sample 
container,  cooled  to  the  temperature  of  liquid  air,  might  absorb 
some  cf  the  residual  gas,  but  tnis  point  was  tested  before  the  sam- 
ple was  introduced  and  no  effect  detected. 

Special  care  was  taken  to  keep  the  mercury  and  the  glass  cf 
the  McLeod  gauge  clean  to  prevent  friction.  It  was  found  that  upon 
taking  several  readings  at  the  same  pressure,  the  gauge  could  be 
read  within  +2^  except  a t the  low  pressures  and  these  seem  to  check 
well  with  the  higher  readings  as  shown  by  the  curves.  The  accurate 
point  at  the  origin  helped  to  take  care  of  such  errors.  The  read- 
ings of  the  Knudsen  gauge  differ  over  a range  cf  two  or  three  percent 
however,  much  of  this  is  due  to  the  fact  that  the  readings  were 
taken  from  curves  and  a range  of  about  one  percent  could  be  obtained 
by  drawing  a new  curve  for  the  same  points.  Hence,  the  error  of  the 


■ 


. 


• . 

. 

i r.ufi  I :|'V 


. 


i 

. 


■ 

■ 


15 


Knudsen  gauge  was  apparently  within  +2fo.  The  temperature  readings 
apparently  did  net  introduce  an  error  larger  than  2 jo,  since  the 
Knudsen  gauge  would  detect  small  changes.  The  total  error,  therefor*, 
is  within  +6 $>.  The  fact  that  this  is  about  the  variation  of  the  indi- 
vidual readings  from  the  mean  curve,  indicates  that  the  principle 
sources  of  error  have  been  accounted  for,  and  that  the  accuracy  of 
the  data  is  what  one  should  expect  from  the  method  employed. 

The  actual  readings  are  given  on  the  following  pages,  begin- 
ning with  Table  II.  The  two  sets  of  calibration  curves  are  shown  in 
the  form  of  curves  in  order  to  show  hew  the  readings  fit  the  curves. 
The  values  determined  for  the  vapor  pressure  of  mercury  are  shown  in 
Fig. 7,  a smooth  curve  is  drawn  through  the  points.  The  values  for 
each  2°,  beginning  with  0°C  and  taken  from  the  mean  curve  are  given 
in  Table  IX.  . 

In  order  to  compare  results  with  those  of  former  methods. 

Table  I and  the  mean  curves  of  Fig.  8,  will  be  referred  to.  The  data 
for  all  methods  is  given  in  10°  intervals.  In  the  first  place,  if 
the  slope  of  the  curves  is  considered,  the  percent  increase  should 
decrease  as  the  temperature  increases.  The  slope  of  the  present 
data  as  measured  in  this  way,  is  about  a mean  of  the  slope  of  other 
methods.  Van  der  Plaats"  curve  has  such  a slight  rise  from  0°  to 
20°  that  if  it  is  extrapolated  above  20°  it  will  not  agree  with  other 
methods.  This  may  be  accounted  for  by  the  variations  of  his  obser- 
vations. Morley's  curve  rises  faster  but  the  low  values  at  16°,  30° , 
and  40°,  would  make  his  curve  too  low  in  that  region.  The  slope  of 
the  present  data  is  greater  than  that  of  Morley’s  and  agrees  with 
Ramsey  and  Young.  The  methods  of  Morley  and  van  der  Plaats  should 
tend  to  give  values  too  low,  while  the  present  method  should  give 


. . 

■ 

. 


. 

. 

. 


. 


. 


, 


. 

' 


«0 


16 


values  too  high  if  in  error,  and.  yet  the  three  agree  fairly  well  and 
with  that  of  Ramsey  and  Young.  On  the  other  hand,  Knudsen's  method 
would  tend  to  give  values  too  low,  and  it  does  net  3eerr.  probable 
that  the  other  three  methods  could  be  in  error  as  much  as  indicated 
by  Knudsents  data.  His  results  are  approximately  5C$>  lower  over  the 
interval  0°  to  20° C. 


, 


. 


CTiCn^OO  CD  CJ1  tfc*  Cn  CD  01  iP*  03  CD  Cl  tt''  Ol  CD  CD  ^ CD 


17 


TABLE  II 


First  set  of  calibration  data 

Pressures  read  on  the  McLeod  gauge,  and  deflections  on 
Knudsen  gauge.  Shown  graphically  in  Fig.  5 


10.0 


10.0 


10.0 


S.  8 


9.7 


R 

Deflect  ion 

McLeod 

Pressure 

Mean 

14.71 

4.71 

.005 

18.04 

8.04 

.005 

22.02 

12.02 

. 00495 

26.4 

16.4 

. 004S8 

.005 

14.1 

4.1 

.004 

16.98 

6.98 

.004 

20.41 

10.41 

.004 

24.15 

14.  15 

. C0395 

.004 

12.98 

2.98 

. 0026 

15.2 

5.2 

. 00255 

17.81 

7.  81 

. 00255 

20.7 

10.7 

.0025 

, 00255 

11.96 

3. 16 

.0016 

13.6 

3.  8 

.0016 

15.4 

5,6 

.0016 

17.48 

7.68 

.00155 

. 0016 

10.8 

1.1 

. 00075 

11.6 

1.9 

. 00072 

12.58 

13.62 

2.88 

3.92 

. 00067 

.00071 

? 


' 


TABLE 

III 

18 

Data 

for  the 

determination  of 

vapor  pressure  of 

mercury 

at  vari- 

OUt 

temperatures  as 

read 

by  the  Knuds en  Gauge 

First 

Run 

• 

Total  Pressures 

I 

R. 

R 

Deflect  ion 

Pressure 

Mean 

Tempera- 

0 

Curve 

ture 

. 3 

10.1 

13.0 

2.9 

.0024 

.4 

15.1 

5.0 

.00337 

23° 

,5 

17.45 

7.35 

.00235 

. 6 

20. 

9.9 

.0023 

. 002355 

Residual  G 

as  Pressure 

.3 

9.82 

10.05 

.23 

.00012 

.4 

10.  15 

. 33 

.00012 

.5 

10.3 

.48 

. 00011 

.6 

10.5 

.68 

.00011 

.000115 

Total  Pressur 

es 

.3 

10.25 

14.5 

4.25 

.00422 

.4 

17.5 

7.25 

.00422 

29.9° 

.5 

20.9 

10.65 

.00416 

. 6 

24.5 

14.  35 

.00407 

.00416 

.3 

10.45 

14.05 

3, 6 

.00336 

.4 

16.65 

6.2 

.00328 

26.8° 

.5 

19.55 

9.1 

.00324 

.6 

22.65 

12.2 

.00314 

.00323 

. 3 

10.4 

13.  32 

2.92 

. 00243 

.4 

15.46 

5.06 

.0034 

.5 

17.85 

7.45 

.00237 

22.8° 

. 6 

20.4 

10.0 

. 00235 

.00239 

. 3 

10.15 

15.52 

5.37 

. 00694 

34.9° 

,4 

19.22 

9.07 

. 00603 

.5 

23.4 

13.35 

.00575 

. 6 

28.0 

17.85 

.0056 

. 00584 

. 3 

10.32 

11.  7 

1.38 

.0009 

.4 

12.  65 

2.  33 

.00088 

11.8° 

.5 

13.  86 

3.54 

. 0009 

.6 

15.15 

4.83 

.0009 

.000895 

.3 

10.68 

11.7 

1.02 

.00062 

.4 

12.4 

1.72 

.00064 

5.8° 

.5 

13.25 

3.57 

.00062 

,6 

14.  2 

3.52 

.00063 

. 00063 

.3 

10.1 

12.6 

3.5 

.00196 

.4 

14.5 

4.4 

.00196 

20.  3° 

.5 

16.  6 

6.  5 

.00194 

. 6 

18.9 

8.8 

. 00194 

.00195 

12 


TABLE  III  (Continued) 


The  apparatus  was  heated  to  100°  for  a short  time  with 
liquid  air  on  sample  container  to  drive  in  mercury  and 
the  following  residual  pressures  at  24. 3° C.  taken 


I 

Ro 

R 

Deflection 

Pr essur 
Curve 

. 3 

10.35 

10.4 

.15 

.00008 

.4 

10.5 

.25 

. 00002 

.5 

10.63 

.37 

. 000088 

. 6 

10.  75 

.5 

. 00008 

M ean 


. 000085 


Tempera- 

ture 


Applying  Charles  Law,  the  residual  pressure  at 
various  temperatures  was  calculated 


5° 00008 

10° 0000813 

15° 0000835 

20c  ......  . . 0000858 

25°  ......  , .000085 

50°  0000865 

35°  . . 000088 


Oi  cn  go  cn  cn  w 01  oi  if*  co 


20 


TABLE  IV 

Second  Run  of  Data. 


o R 

Deflect  ion 

Pressure 

Mean 

Tempera 

Curve 

ture 

5 13. 44 

3.94 

. 00245 

14.55 

5. 05 

.0024 

23° 

16.9 

7.4 

.00234 

19.6 

10.1 

. 00236 

.00239 

7 11.25 

1.55 

.00103 

13.35 

2.65 

. 00103 

13° 

13.55 

3.85 

.00100 

14.9 

5.2 

.00098 

.00101 

Heated  to  : 

130°  with  liquid  ai 

r cn  container 

and  the 

following  residual 

pressures 

taken. 

75  9.33 

.08 

.00005 

33° 

9.86 

.11 

.000043 

S.  8 

.15 

. 000043 

10.0 

.35 

.00004 

. 000044 

... .. 


O-  O!  03  CD  CJi  03  CD  Ul  03  03  CJ3  ^ 03 


21 


I R0 

9.8 

10.0 
10.0 
9.7 
10.2 

10.  15 


TABLE  V 

Third  Run  of  Bata 
R Deflection 


13.0 

3.2 

15.  3 

5.5 

18.0 

8.3 

30.3 

11.1 

14.  33 

4.32 

17.3 

7.3 

20.7 

10.7 

34.5 

14.  5 

15.0 

5.0 

18.55 

8.55 

22,5 

12.5 

26.75 

16.75 

Pressure  Mean  Temp 

Curve  tu 

.00277 

.00274  25° 

.00276 

.00273  .00275 

. 00432 

.00438  30.8° 

.00423 

.00416  .00427 

.0055 

.00556  34.3° 

.0054 

.00514  .00540 


11.05 

1.  35 

12.03 

2.32 

13.19 

3.  43 

14.5 

4.8 

10.8 

.6 

11.17 

.37 

11.7 

1.5 

12.35 

2.15 

.00087 
.00088 
. 00089 
,00088 

.00033 

.00036 

.00036 

.00036 


y precept ible 
.00002 
.00003 
.00003 


11.6° 

.00088 

-.7° 

.00035 

.00002 


Residual  Pressure 

deflection  hardl 
10.19  .04 

10.33  .08 

10.38  .13 


H CD 


TABLE  VI 


22 


Second  Set  of  Calibration  Data 


I 

R0 

R 

Deflection 

Pressure 

(McLeod) 

Mean 

Tempera- 

ture 

. 3 

10.  12 

13.97 

3.85 

.0037 

.4 

16.  8 

6.  68 

.00365 

. 003675 

.5 

20.1 

9.98 

.6 

23.65 

13.53 

. 3 

10.  12 

12.67 

2.55 

.002 

.4 

14.5 

4.38 

.002 

.002 

.5 

16.  78 

6 . 66 

. 6 

19.16 

9.04 

. 3 

10.12 

11.8 

1.68 

.00105 

.4 

13.08 

2.S6 

.0011 

.5 

14.5 

4.38 

,0011 

. 00108 

.3 

10.  OS 

11.  7 

1.08 

.00068 

.4 

11.97 

1.88 

.0006 

. 00064 

.5 

12.  89 

2.  8 

. 6 

13.9 

3.81 

TABLE  VII 

Data 

on  Second  Sample 

I 

*0 

R 

Deflection 

Pressure 

Mean 

Tempera- 

Curve 

tur  e 

.3 

10.5 

14.0 

3.5 

.00318 

.4 

16.5 

6.0 

.00316 

25.  6C 

.5 

19.6 

9.1 

.00320 

. 6 

22.6 

12.1 

.00316 

.00316 

.3 

10.6 

14.  7 

4.1 

. 00402 

.4 

17.  75 

7.15 

.00406 

28.6° 

.5 

20.9 

10,3 

.00388 

. 6 

24.4 

13.  8 

.00380 

. 00394 

.3 

10.  85 

12.56 

1.71 

.00112 

.4 

14.0 

3. 15 

.00118 

11.4° 

.5 

15.55 

4.7 

.0012 

. 6 

17.  2 

6,  3b 

.00116 

.00116 

Residual  Pressure 

. 3 

10.4 

1C.  8 

.4 

.00023 

.4 

11.1 

.7 

. 00024 

.5 

11.45 

1.05 

. 00024 

. 6 

11.8 

1.4 

. 00024 

.00024 

,3 

10.65 

13.95 

3.  3 

.0029 

.4 

16.35 

5.7 

.00292 

24° 

.5 

IS.  0 

8.35 

.00281 

. 5 

22.1 

11.45 

.00284 

.00286 

J 

i 


TABLE  VIII 


23 


Values  for  the 

Vapor  Pressure 

of  Mercury  at  Various 

Temperatures 

T emperature 

Pressure 

Temperature 

Pressure 

mm.  mercury 

mm.  mercury 

-.7°  . . . . 

. 00033 

24.0°  . . . 

. . 00262 

5.8°  . . . . 

. 00055 

25.0°  . . . 

. .00273 

11.4°  ...  . 

. 000S2 

25.6°  . . . 

. .00292 

11.6°  . . . . 

.00083 

26.8°  . . . 

. .003145 

11.8°  ...  . 

.000815 

28.6°  . . . 

. .0037 

13.0°  . . . . 

.00097 

29.9°  . . . 

. .004075 

20.3°  ...  . 

.00187 

30.8°  . . . 

. .00425 

22.8°  ...  . 

. 00230 

34.3°  . . . 

. . 00538 

23.0°  ...  . 

. 00224 

34.9°  . . . 

. .00575 

23.0°  . . . . 

. 00235 

TABLE  IX 

Values  for  Each  2C  as  Taken  From  Mean  Curve 


0.0°  ...  . 

.000350 

2.0°  ...  . 

.000412 

4.0°  . . . . 

.000487 

6.0°  ...  . 

.000572 

8.0°  ...  . 

.000662 

10.0°  ...  . 

.000775 

12.0°  . . . . 

.000895 

14.0°  ...  . 

.00105 

16.0°  . . . . 

.00126 

18.0°  ...  . 

.00150 

20.0°  . . . . 

.00182 

22.0°  . . . . 

. 00214 

24.0°  . . . . 

. 00334 

36.0°  . . . . 

. 003 

28.0°  . . . . 

. 0035 

30.0°  ...  . 

. 00407 

32.0°  . . . . 

. 00467 

34.0°  . . . . 

. 00535 

36.0°  . . . . 

. 00607 

38.0°  .... 

. 00693 

40.0°  ...  . 

. 008 

Fig.  5 


Fig.  S 


Fig.? 


27 


Fig.  8 


38 


IV  CONCLUSIONS 

The  following  conclusions  m ay  be  drawn: 

1.  A direct  method  for  the  measurement  of  mercury  vapor 
pressure  has  been  employed  in  which  advantage  was  taken  of  the  pres- 
ent day  methods  of  obtaining  a high  vacuum,  and  its  measurement  by 
means  of  the  Knuds en  gauge. 

3.  Nineteen  readings  on  the  vapor  pressure  of  mercury  have 
been  taken  between  the  temperatures  of  -.7°  and  34.9°  Centigrade. 
These  values  lie  within  ±<ofo  of  a mean  curve. 

3.  A criticism  of  the  method  indicates  that  it  should  not  be 
in  error  by  more  than  ±6fo}  except  for  impurities  and  that  these  have 
been  reduced  to  a minimum  by  the  method  of  purification. 

4.  The  order  of  tne  values  obtained  agrees  fairly  well  with 
those  of  Morley  and  van  der  Plaats;  however,  the  percent  variation 
of  the  actual  observations  is  much  less  in  the  present  method. 

5.  The  slope  of  the  curve  of  the  present  data  is  aocut  a 
mean  of  the  slopes  of  other  methods  and  agrees  with  that  of  Ramsey 
ana  Young  extrapolated  from  higher  temperatures. 

In  conclusion,  I wish  to  thank  Professor  A.P.  Carman  for 
the  use  of  the  facilities  of  the  laboratory,  and  Professor  C.  T. 
Knipp  for  the  interest  he  has  taken  in  the  work  and  for  the  sug- 
gestions offered. 


. 


. 


. . 


. 


VITA 


Charles  Francis  Hill  received  his  early  edu- 
cation in  the  public  schools  of  Illinois,  and  his 
college  preparatory  work  in  the  Eastern  Illinois 
State  Normal  School  from  which  he  graduated  in 
1911.  He  then  entered  the  University  cf  Illinois, 
from  which  ne  received  the  degree  of  A.B. , in  1914. 
From  1914  to  1921  he  has  been  an  assistant  in 
physics  at  the  University  of  Illinois,  doing  part- 
time  graduate  work,  having  received  the  degree  cf 
M . A . in  1916. 


